Price was born in Leyton, England, to Philip Price, a tailor, and Fanny de Solla, a singer. He began work in 1938 as an assistant in a physics laboratory at the South West Essex Technical College, before studying Physics and Mathematics at the University of London, where he received a Bachelor of Science in 1942. He obtained a Doctor of Philosophy in experimental physics from the University of London in 1946.

In 1948 Price worked as a teacher of applied mathematics at Raffles College, Singapore, which was to become part of the National University of Singapore. It was there that he formulated his theory on the exponential growth of science, an idea that occurred to him when he noticed the characteristic logarithmic curve of the Philosophical Transactions of the Royal Society between 1665 and 1850, which he had stacked against his wall at home while Raffles College had its library built.

After three years, Price sought appointment as a lecturer at University of Cambridge, but was told to enroll as a student. He returned to England to work on a second Ph.D., in the history of science. During his Ph.D. studies, he discovered The Equatorie of the Planetis, a Peterhouse manuscript in Cambridge University Library, written in Middle English, which he and attributed to Geoffrey Chaucer. It is now attributed to a St Albans monk called John Westwyk

Around 1950, Price adopted his mother's Sephardic name, "de Solla", as a middle name. He was a "British Atheist ... from a rather well-known Sephardic Jewish family", and although his Danish wife, Ellen, had been christened as a Lutheran, he did not, according to their son Mark, regard their marriage as "mixed", because they were both atheists.

After obtaining his second doctorate, Price found advancement difficult in England. One colleague alleged that Price, who came from a lower class background, was "not socially house-trained," and he suspected that he was turned down for university positions for personal reasons.[5] Price decided to move to the United States, where he served as a consultant to the Smithsonian Institution, and as a fellow at the Institute for Advanced Study in Princeton, New Jersey. His next post was at Yale University, where he worked until his death, serving as the Avalon Professor of the History of Science, and as chair of a new department that encompassed the histories of science, technology, and medicine.

In 1984, Price received, posthumously, the ASIS Research Award for outstanding contributions in the field of information science.

Since 1984, the Derek de Solla Price Memorial Medal is awarded by the International Society for Scientometrics and Informetrics to scientists with outstanding contributions to the fields of quantitative studies of science.